# Haskell - Expressions

The following illustrates some haskell basics. It can be reproduced using `ghci`.

## Types, Literals, and Constants along with Arithmetic and Boolean Operations

Expression | Type (:t) | Value | Comment 
--- | --- | --- | -------- 
`2` | `Num a => a` | `2` |
`2.03` | `Fractional a => a` | `2.3` |
`'c'` | `Char` | `'c'`
`"hallo"` | `String` | `"hallo"` |
`True` | `Bool` | `True` |
`x=5` | `Num a => a` | `5` | Constant named `x`
`2 + 3` | `Num a => a` | `5` | Similar `-,*,^`
`2 / 3` | `Fractional a => a` | `0.6666666666666666` |
`1 > 2` | `Bool` | `False` | Similar `<, <=, >=, ==, /=`
`True && False` | `Bool` | `False` | Similar `\|\|,not`
`((2+3)*5 > 1) \|\| not (1 > 2)` | `Bool` | `True` | Right part is not evaluated due to lazy evaluation

## Unary Functions

Expression | Type (:t) | Value | Comment 
--- | --- | --- | -------- 
`sqrt(4)` | `Floating a => a` | `2.0` |
`sqrt 4` | `Floating a => a` | `2.0` | Similar `abs,negate,signum,recip`
`sqrt` | `Floating a => a -> a` | |
`sqrt 3^2 + 4^2` | `Floating a => a` | `19.0` |
`sqrt (3^2 + 4^2)` | `Floating a => a` | `5.0` |
`negate(sqrt (3^2 + 4^2))` | `Floating a => a` | `-5.0` |
`negate $ sqrt (3^2 + 4^2)` | `Floating a => a`| `-5.0` | Function **application** operator `$`
`(negate . sqrt) (3^2 + 4^2)`| `Floating a => a`| `-5.0` | Function **composition** operator `.` Reads `negate` **after** `negate . sqrt` | 
`(negate . length) "hallo"` | `Int` | `-5` | 
`negatedRoot = negate . sqrt` | `Floating c => c -> c` | | Constant named `negatedRoot`

## Binary Functions

Expression | Type (:t) | Value | Comment 
--- | --- | --- | -------- 
`div 8 4` | `Integral a => a` | `2` | Similar `mod,gcd,lcm,not`
``8 `div` 4`` | `Integral a => a` | `2` | **Infix** notation using backticks
`8 + 4` | `Num a => a` | `12` | `-,*,^,<, <=, >=, ==, /=`
`(+) 8 4` | `Num a => a` | `12` | **Prefix** notation using parenthesis
`div` | `Integral a => a -> a -> a` | | **Currying** represents multi-argument functions as a chain of single-argument functions |
`div 8` | `Integral a => a -> a` | | binds the **first** argument; Similar `(8/),(8*),(8+),(8-)` |
`div8bySomething = div 8` | `Integral a => a -> a` | | 
`div8bySomething 4` | `Integral a => a` | `2` |
`uncurry div` | `Integral c => (c, c) -> c` | | accepts a single tuple argument
`uncurry div (8,4)` | `Integral c => c` | `2` | 
`uncurry` | `(a -> b -> c) -> (a, b) -> c`| |
`` (`div` 4) `` | `Integral a => a -> a` | | **Sectioning** binds the **second** argument of infix functions; Similar `(/8),(*8),(+8),(-8)` |
``divSomethingBy4 = (`div` 4)`` | `Integral a => a -> a` | | 
`divSomethingBy4 8` | `Integral a => a` | `2` | 

## Tuples

Expression | Type (:t) | Value | Comment 
--- | --- | --- | -------- 
`(1, 2)` | `(Num a, Num b) => (a, b)` | `(1, 2)` |
`(1, "hello", True)` | `(Num a => (a, String, Bool)` | `(1, "hello", True)` |
`fst (1, 2)` | `Num a => a` | `1` |
`snd (1, 2)` | `Num b => b` | `2` |
`(,) 1 2` | `Num a => a -> a -> (a, a)` | `(1, 2)` |

## Strings

Expression | Type (:t) | Value | Comment 
--- | --- | --- | -------- 
`"hello" ++ " world"` | `String` | `"hello world"` | String concatenation
`length "hello"` | `Int` | `5` | Length of the string
`null ""` | `Bool` | `True` | Checks if the string is empty

## Control Structures

## Lists